# HG changeset patch # User wenzelm # Date 1159733963 -7200 # Node ID 58693343905f5295ac96fa2dcf69ca339641b6fe # Parent cb6ae81dd0beb228d69b4cfd7d3b8d56d183ec5c removed obsolete Datatype_Universe.thy (cf. Datatype.thy); diff -r cb6ae81dd0be -r 58693343905f src/HOL/Datatype_Universe.thy --- a/src/HOL/Datatype_Universe.thy Sun Oct 01 22:19:21 2006 +0200 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,634 +0,0 @@ -(* Title: HOL/Datatype_Universe.thy - ID: $Id$ - Author: Lawrence C Paulson, Cambridge University Computer Laboratory - Copyright 1993 University of Cambridge - -Could <*> be generalized to a general summation (Sigma)? -*) - -header{*Analogues of the Cartesian Product and Disjoint Sum for Datatypes*} - -theory Datatype_Universe -imports NatArith Sum_Type -begin - - -typedef (Node) - ('a,'b) node = "{p. EX f x k. p = (f::nat=>'b+nat, x::'a+nat) & f k = Inr 0}" - --{*it is a subtype of @{text "(nat=>'b+nat) * ('a+nat)"}*} - by auto - -text{*Datatypes will be represented by sets of type @{text node}*} - -types 'a item = "('a, unit) node set" - ('a, 'b) dtree = "('a, 'b) node set" - -consts - apfst :: "['a=>'c, 'a*'b] => 'c*'b" - Push :: "[('b + nat), nat => ('b + nat)] => (nat => ('b + nat))" - - Push_Node :: "[('b + nat), ('a, 'b) node] => ('a, 'b) node" - ndepth :: "('a, 'b) node => nat" - - Atom :: "('a + nat) => ('a, 'b) dtree" - Leaf :: "'a => ('a, 'b) dtree" - Numb :: "nat => ('a, 'b) dtree" - Scons :: "[('a, 'b) dtree, ('a, 'b) dtree] => ('a, 'b) dtree" - In0 :: "('a, 'b) dtree => ('a, 'b) dtree" - In1 :: "('a, 'b) dtree => ('a, 'b) dtree" - Lim :: "('b => ('a, 'b) dtree) => ('a, 'b) dtree" - - ntrunc :: "[nat, ('a, 'b) dtree] => ('a, 'b) dtree" - - uprod :: "[('a, 'b) dtree set, ('a, 'b) dtree set]=> ('a, 'b) dtree set" - usum :: "[('a, 'b) dtree set, ('a, 'b) dtree set]=> ('a, 'b) dtree set" - - Split :: "[[('a, 'b) dtree, ('a, 'b) dtree]=>'c, ('a, 'b) dtree] => 'c" - Case :: "[[('a, 'b) dtree]=>'c, [('a, 'b) dtree]=>'c, ('a, 'b) dtree] => 'c" - - dprod :: "[(('a, 'b) dtree * ('a, 'b) dtree)set, (('a, 'b) dtree * ('a, 'b) dtree)set] - => (('a, 'b) dtree * ('a, 'b) dtree)set" - dsum :: "[(('a, 'b) dtree * ('a, 'b) dtree)set, (('a, 'b) dtree * ('a, 'b) dtree)set] - => (('a, 'b) dtree * ('a, 'b) dtree)set" - - -defs - - Push_Node_def: "Push_Node == (%n x. Abs_Node (apfst (Push n) (Rep_Node x)))" - - (*crude "lists" of nats -- needed for the constructions*) - apfst_def: "apfst == (%f (x,y). (f(x),y))" - Push_def: "Push == (%b h. nat_case b h)" - - (** operations on S-expressions -- sets of nodes **) - - (*S-expression constructors*) - Atom_def: "Atom == (%x. {Abs_Node((%k. Inr 0, x))})" - Scons_def: "Scons M N == (Push_Node (Inr 1) ` M) Un (Push_Node (Inr (Suc 1)) ` N)" - - (*Leaf nodes, with arbitrary or nat labels*) - Leaf_def: "Leaf == Atom o Inl" - Numb_def: "Numb == Atom o Inr" - - (*Injections of the "disjoint sum"*) - In0_def: "In0(M) == Scons (Numb 0) M" - In1_def: "In1(M) == Scons (Numb 1) M" - - (*Function spaces*) - Lim_def: "Lim f == Union {z. ? x. z = Push_Node (Inl x) ` (f x)}" - - (*the set of nodes with depth less than k*) - ndepth_def: "ndepth(n) == (%(f,x). LEAST k. f k = Inr 0) (Rep_Node n)" - ntrunc_def: "ntrunc k N == {n. n:N & ndepth(n) R - |] ==> R" -by (force simp add: apfst_def) - -(** Push -- an injection, analogous to Cons on lists **) - -lemma Push_inject1: "Push i f = Push j g ==> i=j" -apply (simp add: Push_def expand_fun_eq) -apply (drule_tac x=0 in spec, simp) -done - -lemma Push_inject2: "Push i f = Push j g ==> f=g" -apply (auto simp add: Push_def expand_fun_eq) -apply (drule_tac x="Suc x" in spec, simp) -done - -lemma Push_inject: - "[| Push i f =Push j g; [| i=j; f=g |] ==> P |] ==> P" -by (blast dest: Push_inject1 Push_inject2) - -lemma Push_neq_K0: "Push (Inr (Suc k)) f = (%z. Inr 0) ==> P" -by (auto simp add: Push_def expand_fun_eq split: nat.split_asm) - -lemmas Abs_Node_inj = Abs_Node_inject [THEN [2] rev_iffD1, standard] - - -(*** Introduction rules for Node ***) - -lemma Node_K0_I: "(%k. Inr 0, a) : Node" -by (simp add: Node_def) - -lemma Node_Push_I: "p: Node ==> apfst (Push i) p : Node" -apply (simp add: Node_def Push_def) -apply (fast intro!: apfst_conv nat_case_Suc [THEN trans]) -done - - -subsection{*Freeness: Distinctness of Constructors*} - -(** Scons vs Atom **) - -lemma Scons_not_Atom [iff]: "Scons M N \ Atom(a)" -apply (simp add: Atom_def Scons_def Push_Node_def One_nat_def) -apply (blast intro: Node_K0_I Rep_Node [THEN Node_Push_I] - dest!: Abs_Node_inj - elim!: apfst_convE sym [THEN Push_neq_K0]) -done - -lemmas Atom_not_Scons = Scons_not_Atom [THEN not_sym, standard] -declare Atom_not_Scons [iff] - -(*** Injectiveness ***) - -(** Atomic nodes **) - -lemma inj_Atom: "inj(Atom)" -apply (simp add: Atom_def) -apply (blast intro!: inj_onI Node_K0_I dest!: Abs_Node_inj) -done -lemmas Atom_inject = inj_Atom [THEN injD, standard] - -lemma Atom_Atom_eq [iff]: "(Atom(a)=Atom(b)) = (a=b)" -by (blast dest!: Atom_inject) - -lemma inj_Leaf: "inj(Leaf)" -apply (simp add: Leaf_def o_def) -apply (rule inj_onI) -apply (erule Atom_inject [THEN Inl_inject]) -done - -lemmas Leaf_inject = inj_Leaf [THEN injD, standard] -declare Leaf_inject [dest!] - -lemma inj_Numb: "inj(Numb)" -apply (simp add: Numb_def o_def) -apply (rule inj_onI) -apply (erule Atom_inject [THEN Inr_inject]) -done - -lemmas Numb_inject = inj_Numb [THEN injD, standard] -declare Numb_inject [dest!] - - -(** Injectiveness of Push_Node **) - -lemma Push_Node_inject: - "[| Push_Node i m =Push_Node j n; [| i=j; m=n |] ==> P - |] ==> P" -apply (simp add: Push_Node_def) -apply (erule Abs_Node_inj [THEN apfst_convE]) -apply (rule Rep_Node [THEN Node_Push_I])+ -apply (erule sym [THEN apfst_convE]) -apply (blast intro: Rep_Node_inject [THEN iffD1] trans sym elim!: Push_inject) -done - - -(** Injectiveness of Scons **) - -lemma Scons_inject_lemma1: "Scons M N <= Scons M' N' ==> M<=M'" -apply (simp add: Scons_def One_nat_def) -apply (blast dest!: Push_Node_inject) -done - -lemma Scons_inject_lemma2: "Scons M N <= Scons M' N' ==> N<=N'" -apply (simp add: Scons_def One_nat_def) -apply (blast dest!: Push_Node_inject) -done - -lemma Scons_inject1: "Scons M N = Scons M' N' ==> M=M'" -apply (erule equalityE) -apply (iprover intro: equalityI Scons_inject_lemma1) -done - -lemma Scons_inject2: "Scons M N = Scons M' N' ==> N=N'" -apply (erule equalityE) -apply (iprover intro: equalityI Scons_inject_lemma2) -done - -lemma Scons_inject: - "[| Scons M N = Scons M' N'; [| M=M'; N=N' |] ==> P |] ==> P" -by (iprover dest: Scons_inject1 Scons_inject2) - -lemma Scons_Scons_eq [iff]: "(Scons M N = Scons M' N') = (M=M' & N=N')" -by (blast elim!: Scons_inject) - -(*** Distinctness involving Leaf and Numb ***) - -(** Scons vs Leaf **) - -lemma Scons_not_Leaf [iff]: "Scons M N \ Leaf(a)" -by (simp add: Leaf_def o_def Scons_not_Atom) - -lemmas Leaf_not_Scons = Scons_not_Leaf [THEN not_sym, standard] -declare Leaf_not_Scons [iff] - -(** Scons vs Numb **) - -lemma Scons_not_Numb [iff]: "Scons M N \ Numb(k)" -by (simp add: Numb_def o_def Scons_not_Atom) - -lemmas Numb_not_Scons = Scons_not_Numb [THEN not_sym, standard] -declare Numb_not_Scons [iff] - - -(** Leaf vs Numb **) - -lemma Leaf_not_Numb [iff]: "Leaf(a) \ Numb(k)" -by (simp add: Leaf_def Numb_def) - -lemmas Numb_not_Leaf = Leaf_not_Numb [THEN not_sym, standard] -declare Numb_not_Leaf [iff] - - -(*** ndepth -- the depth of a node ***) - -lemma ndepth_K0: "ndepth (Abs_Node(%k. Inr 0, x)) = 0" -by (simp add: ndepth_def Node_K0_I [THEN Abs_Node_inverse] Least_equality) - -lemma ndepth_Push_Node_aux: - "nat_case (Inr (Suc i)) f k = Inr 0 --> Suc(LEAST x. f x = Inr 0) <= k" -apply (induct_tac "k", auto) -apply (erule Least_le) -done - -lemma ndepth_Push_Node: - "ndepth (Push_Node (Inr (Suc i)) n) = Suc(ndepth(n))" -apply (insert Rep_Node [of n, unfolded Node_def]) -apply (auto simp add: ndepth_def Push_Node_def - Rep_Node [THEN Node_Push_I, THEN Abs_Node_inverse]) -apply (rule Least_equality) -apply (auto simp add: Push_def ndepth_Push_Node_aux) -apply (erule LeastI) -done - - -(*** ntrunc applied to the various node sets ***) - -lemma ntrunc_0 [simp]: "ntrunc 0 M = {}" -by (simp add: ntrunc_def) - -lemma ntrunc_Atom [simp]: "ntrunc (Suc k) (Atom a) = Atom(a)" -by (auto simp add: Atom_def ntrunc_def ndepth_K0) - -lemma ntrunc_Leaf [simp]: "ntrunc (Suc k) (Leaf a) = Leaf(a)" -by (simp add: Leaf_def o_def ntrunc_Atom) - -lemma ntrunc_Numb [simp]: "ntrunc (Suc k) (Numb i) = Numb(i)" -by (simp add: Numb_def o_def ntrunc_Atom) - -lemma ntrunc_Scons [simp]: - "ntrunc (Suc k) (Scons M N) = Scons (ntrunc k M) (ntrunc k N)" -by (auto simp add: Scons_def ntrunc_def One_nat_def ndepth_Push_Node) - - - -(** Injection nodes **) - -lemma ntrunc_one_In0 [simp]: "ntrunc (Suc 0) (In0 M) = {}" -apply (simp add: In0_def) -apply (simp add: Scons_def) -done - -lemma ntrunc_In0 [simp]: "ntrunc (Suc(Suc k)) (In0 M) = In0 (ntrunc (Suc k) M)" -by (simp add: In0_def) - -lemma ntrunc_one_In1 [simp]: "ntrunc (Suc 0) (In1 M) = {}" -apply (simp add: In1_def) -apply (simp add: Scons_def) -done - -lemma ntrunc_In1 [simp]: "ntrunc (Suc(Suc k)) (In1 M) = In1 (ntrunc (Suc k) M)" -by (simp add: In1_def) - - -subsection{*Set Constructions*} - - -(*** Cartesian Product ***) - -lemma uprodI [intro!]: "[| M:A; N:B |] ==> Scons M N : uprod A B" -by (simp add: uprod_def) - -(*The general elimination rule*) -lemma uprodE [elim!]: - "[| c : uprod A B; - !!x y. [| x:A; y:B; c = Scons x y |] ==> P - |] ==> P" -by (auto simp add: uprod_def) - - -(*Elimination of a pair -- introduces no eigenvariables*) -lemma uprodE2: "[| Scons M N : uprod A B; [| M:A; N:B |] ==> P |] ==> P" -by (auto simp add: uprod_def) - - -(*** Disjoint Sum ***) - -lemma usum_In0I [intro]: "M:A ==> In0(M) : usum A B" -by (simp add: usum_def) - -lemma usum_In1I [intro]: "N:B ==> In1(N) : usum A B" -by (simp add: usum_def) - -lemma usumE [elim!]: - "[| u : usum A B; - !!x. [| x:A; u=In0(x) |] ==> P; - !!y. [| y:B; u=In1(y) |] ==> P - |] ==> P" -by (auto simp add: usum_def) - - -(** Injection **) - -lemma In0_not_In1 [iff]: "In0(M) \ In1(N)" -by (auto simp add: In0_def In1_def One_nat_def) - -lemmas In1_not_In0 = In0_not_In1 [THEN not_sym, standard] -declare In1_not_In0 [iff] - -lemma In0_inject: "In0(M) = In0(N) ==> M=N" -by (simp add: In0_def) - -lemma In1_inject: "In1(M) = In1(N) ==> M=N" -by (simp add: In1_def) - -lemma In0_eq [iff]: "(In0 M = In0 N) = (M=N)" -by (blast dest!: In0_inject) - -lemma In1_eq [iff]: "(In1 M = In1 N) = (M=N)" -by (blast dest!: In1_inject) - -lemma inj_In0: "inj In0" -by (blast intro!: inj_onI) - -lemma inj_In1: "inj In1" -by (blast intro!: inj_onI) - - -(*** Function spaces ***) - -lemma Lim_inject: "Lim f = Lim g ==> f = g" -apply (simp add: Lim_def) -apply (rule ext) -apply (blast elim!: Push_Node_inject) -done - - -(*** proving equality of sets and functions using ntrunc ***) - -lemma ntrunc_subsetI: "ntrunc k M <= M" -by (auto simp add: ntrunc_def) - -lemma ntrunc_subsetD: "(!!k. ntrunc k M <= N) ==> M<=N" -by (auto simp add: ntrunc_def) - -(*A generalized form of the take-lemma*) -lemma ntrunc_equality: "(!!k. ntrunc k M = ntrunc k N) ==> M=N" -apply (rule equalityI) -apply (rule_tac [!] ntrunc_subsetD) -apply (rule_tac [!] ntrunc_subsetI [THEN [2] subset_trans], auto) -done - -lemma ntrunc_o_equality: - "[| !!k. (ntrunc(k) o h1) = (ntrunc(k) o h2) |] ==> h1=h2" -apply (rule ntrunc_equality [THEN ext]) -apply (simp add: expand_fun_eq) -done - - -(*** Monotonicity ***) - -lemma uprod_mono: "[| A<=A'; B<=B' |] ==> uprod A B <= uprod A' B'" -by (simp add: uprod_def, blast) - -lemma usum_mono: "[| A<=A'; B<=B' |] ==> usum A B <= usum A' B'" -by (simp add: usum_def, blast) - -lemma Scons_mono: "[| M<=M'; N<=N' |] ==> Scons M N <= Scons M' N'" -by (simp add: Scons_def, blast) - -lemma In0_mono: "M<=N ==> In0(M) <= In0(N)" -by (simp add: In0_def subset_refl Scons_mono) - -lemma In1_mono: "M<=N ==> In1(M) <= In1(N)" -by (simp add: In1_def subset_refl Scons_mono) - - -(*** Split and Case ***) - -lemma Split [simp]: "Split c (Scons M N) = c M N" -by (simp add: Split_def) - -lemma Case_In0 [simp]: "Case c d (In0 M) = c(M)" -by (simp add: Case_def) - -lemma Case_In1 [simp]: "Case c d (In1 N) = d(N)" -by (simp add: Case_def) - - - -(**** UN x. B(x) rules ****) - -lemma ntrunc_UN1: "ntrunc k (UN x. f(x)) = (UN x. ntrunc k (f x))" -by (simp add: ntrunc_def, blast) - -lemma Scons_UN1_x: "Scons (UN x. f x) M = (UN x. Scons (f x) M)" -by (simp add: Scons_def, blast) - -lemma Scons_UN1_y: "Scons M (UN x. f x) = (UN x. Scons M (f x))" -by (simp add: Scons_def, blast) - -lemma In0_UN1: "In0(UN x. f(x)) = (UN x. In0(f(x)))" -by (simp add: In0_def Scons_UN1_y) - -lemma In1_UN1: "In1(UN x. f(x)) = (UN x. In1(f(x)))" -by (simp add: In1_def Scons_UN1_y) - - -(*** Equality for Cartesian Product ***) - -lemma dprodI [intro!]: - "[| (M,M'):r; (N,N'):s |] ==> (Scons M N, Scons M' N') : dprod r s" -by (auto simp add: dprod_def) - -(*The general elimination rule*) -lemma dprodE [elim!]: - "[| c : dprod r s; - !!x y x' y'. [| (x,x') : r; (y,y') : s; - c = (Scons x y, Scons x' y') |] ==> P - |] ==> P" -by (auto simp add: dprod_def) - - -(*** Equality for Disjoint Sum ***) - -lemma dsum_In0I [intro]: "(M,M'):r ==> (In0(M), In0(M')) : dsum r s" -by (auto simp add: dsum_def) - -lemma dsum_In1I [intro]: "(N,N'):s ==> (In1(N), In1(N')) : dsum r s" -by (auto simp add: dsum_def) - -lemma dsumE [elim!]: - "[| w : dsum r s; - !!x x'. [| (x,x') : r; w = (In0(x), In0(x')) |] ==> P; - !!y y'. [| (y,y') : s; w = (In1(y), In1(y')) |] ==> P - |] ==> P" -by (auto simp add: dsum_def) - - -(*** Monotonicity ***) - -lemma dprod_mono: "[| r<=r'; s<=s' |] ==> dprod r s <= dprod r' s'" -by blast - -lemma dsum_mono: "[| r<=r'; s<=s' |] ==> dsum r s <= dsum r' s'" -by blast - - -(*** Bounding theorems ***) - -lemma dprod_Sigma: "(dprod (A <*> B) (C <*> D)) <= (uprod A C) <*> (uprod B D)" -by blast - -lemmas dprod_subset_Sigma = subset_trans [OF dprod_mono dprod_Sigma, standard] - -(*Dependent version*) -lemma dprod_subset_Sigma2: - "(dprod (Sigma A B) (Sigma C D)) <= - Sigma (uprod A C) (Split (%x y. uprod (B x) (D y)))" -by auto - -lemma dsum_Sigma: "(dsum (A <*> B) (C <*> D)) <= (usum A C) <*> (usum B D)" -by blast - -lemmas dsum_subset_Sigma = subset_trans [OF dsum_mono dsum_Sigma, standard] - - -(*** Domain ***) - -lemma Domain_dprod [simp]: "Domain (dprod r s) = uprod (Domain r) (Domain s)" -by auto - -lemma Domain_dsum [simp]: "Domain (dsum r s) = usum (Domain r) (Domain s)" -by auto - - -subsection {* Finishing the datatype package setup *} - -text {* Belongs to theory @{text Datatype_Universe}; hides popular names. *} -hide (open) const Push Node Atom Leaf Numb Lim Split Case -hide (open) type node item - -ML -{* -val apfst_conv = thm "apfst_conv"; -val apfst_convE = thm "apfst_convE"; -val Push_inject1 = thm "Push_inject1"; -val Push_inject2 = thm "Push_inject2"; -val Push_inject = thm "Push_inject"; -val Push_neq_K0 = thm "Push_neq_K0"; -val Abs_Node_inj = thm "Abs_Node_inj"; -val Node_K0_I = thm "Node_K0_I"; -val Node_Push_I = thm "Node_Push_I"; -val Scons_not_Atom = thm "Scons_not_Atom"; -val Atom_not_Scons = thm "Atom_not_Scons"; -val inj_Atom = thm "inj_Atom"; -val Atom_inject = thm "Atom_inject"; -val Atom_Atom_eq = thm "Atom_Atom_eq"; -val inj_Leaf = thm "inj_Leaf"; -val Leaf_inject = thm "Leaf_inject"; -val inj_Numb = thm "inj_Numb"; -val Numb_inject = thm "Numb_inject"; -val Push_Node_inject = thm "Push_Node_inject"; -val Scons_inject1 = thm "Scons_inject1"; -val Scons_inject2 = thm "Scons_inject2"; -val Scons_inject = thm "Scons_inject"; -val Scons_Scons_eq = thm "Scons_Scons_eq"; -val Scons_not_Leaf = thm "Scons_not_Leaf"; -val Leaf_not_Scons = thm "Leaf_not_Scons"; -val Scons_not_Numb = thm "Scons_not_Numb"; -val Numb_not_Scons = thm "Numb_not_Scons"; -val Leaf_not_Numb = thm "Leaf_not_Numb"; -val Numb_not_Leaf = thm "Numb_not_Leaf"; -val ndepth_K0 = thm "ndepth_K0"; -val ndepth_Push_Node_aux = thm "ndepth_Push_Node_aux"; -val ndepth_Push_Node = thm "ndepth_Push_Node"; -val ntrunc_0 = thm "ntrunc_0"; -val ntrunc_Atom = thm "ntrunc_Atom"; -val ntrunc_Leaf = thm "ntrunc_Leaf"; -val ntrunc_Numb = thm "ntrunc_Numb"; -val ntrunc_Scons = thm "ntrunc_Scons"; -val ntrunc_one_In0 = thm "ntrunc_one_In0"; -val ntrunc_In0 = thm "ntrunc_In0"; -val ntrunc_one_In1 = thm "ntrunc_one_In1"; -val ntrunc_In1 = thm "ntrunc_In1"; -val uprodI = thm "uprodI"; -val uprodE = thm "uprodE"; -val uprodE2 = thm "uprodE2"; -val usum_In0I = thm "usum_In0I"; -val usum_In1I = thm "usum_In1I"; -val usumE = thm "usumE"; -val In0_not_In1 = thm "In0_not_In1"; -val In1_not_In0 = thm "In1_not_In0"; -val In0_inject = thm "In0_inject"; -val In1_inject = thm "In1_inject"; -val In0_eq = thm "In0_eq"; -val In1_eq = thm "In1_eq"; -val inj_In0 = thm "inj_In0"; -val inj_In1 = thm "inj_In1"; -val Lim_inject = thm "Lim_inject"; -val ntrunc_subsetI = thm "ntrunc_subsetI"; -val ntrunc_subsetD = thm "ntrunc_subsetD"; -val ntrunc_equality = thm "ntrunc_equality"; -val ntrunc_o_equality = thm "ntrunc_o_equality"; -val uprod_mono = thm "uprod_mono"; -val usum_mono = thm "usum_mono"; -val Scons_mono = thm "Scons_mono"; -val In0_mono = thm "In0_mono"; -val In1_mono = thm "In1_mono"; -val Split = thm "Split"; -val Case_In0 = thm "Case_In0"; -val Case_In1 = thm "Case_In1"; -val ntrunc_UN1 = thm "ntrunc_UN1"; -val Scons_UN1_x = thm "Scons_UN1_x"; -val Scons_UN1_y = thm "Scons_UN1_y"; -val In0_UN1 = thm "In0_UN1"; -val In1_UN1 = thm "In1_UN1"; -val dprodI = thm "dprodI"; -val dprodE = thm "dprodE"; -val dsum_In0I = thm "dsum_In0I"; -val dsum_In1I = thm "dsum_In1I"; -val dsumE = thm "dsumE"; -val dprod_mono = thm "dprod_mono"; -val dsum_mono = thm "dsum_mono"; -val dprod_Sigma = thm "dprod_Sigma"; -val dprod_subset_Sigma = thm "dprod_subset_Sigma"; -val dprod_subset_Sigma2 = thm "dprod_subset_Sigma2"; -val dsum_Sigma = thm "dsum_Sigma"; -val dsum_subset_Sigma = thm "dsum_subset_Sigma"; -val Domain_dprod = thm "Domain_dprod"; -val Domain_dsum = thm "Domain_dsum"; -*} - -end diff -r cb6ae81dd0be -r 58693343905f src/HOL/Induct/SList.thy --- a/src/HOL/Induct/SList.thy Sun Oct 01 22:19:21 2006 +0200 +++ b/src/HOL/Induct/SList.thy Sun Oct 01 22:19:23 2006 +0200 @@ -56,8 +56,8 @@ by (blast intro: list.NIL_I) abbreviation - "Case == Datatype_Universe.Case" - "Split == Datatype_Universe.Split" + "Case == Datatype.Case" + "Split == Datatype.Split" definition List_case :: "['b, ['a item, 'a item]=>'b, 'a item] => 'b" diff -r cb6ae81dd0be -r 58693343905f src/HOL/Induct/Sexp.thy --- a/src/HOL/Induct/Sexp.thy Sun Oct 01 22:19:21 2006 +0200 +++ b/src/HOL/Induct/Sexp.thy Sun Oct 01 22:19:23 2006 +0200 @@ -10,10 +10,10 @@ theory Sexp imports Main begin types - 'a item = "'a Datatype_Universe.item" + 'a item = "'a Datatype.item" abbreviation - "Leaf == Datatype_Universe.Leaf" - "Numb == Datatype_Universe.Numb" + "Leaf == Datatype.Leaf" + "Numb == Datatype.Numb" consts sexp :: "'a item set" diff -r cb6ae81dd0be -r 58693343905f src/HOL/IsaMakefile --- a/src/HOL/IsaMakefile Sun Oct 01 22:19:21 2006 +0200 +++ b/src/HOL/IsaMakefile Sun Oct 01 22:19:23 2006 +0200 @@ -85,7 +85,7 @@ $(SRC)/TFL/thry.ML $(SRC)/TFL/usyntax.ML $(SRC)/TFL/utils.ML \ Tools/res_atpset.ML \ Binomial.thy Datatype.ML Datatype.thy \ - Datatype_Universe.thy Divides.thy \ + Divides.thy \ Equiv_Relations.thy Extraction.thy Finite_Set.ML Finite_Set.thy \ FixedPoint.thy Fun.thy HOL.ML HOL.thy Hilbert_Choice.thy Inductive.thy \ Integ/IntArith.thy Integ/IntDef.thy Integ/IntDiv.thy \ diff -r cb6ae81dd0be -r 58693343905f src/HOL/Library/Coinductive_List.thy --- a/src/HOL/Library/Coinductive_List.thy Sun Oct 01 22:19:21 2006 +0200 +++ b/src/HOL/Library/Coinductive_List.thy Sun Oct 01 22:19:23 2006 +0200 @@ -12,8 +12,8 @@ subsection {* List constructors over the datatype universe *} definition - "NIL = Datatype_Universe.In0 (Datatype_Universe.Numb 0)" - "CONS M N = Datatype_Universe.In1 (Datatype_Universe.Scons M N)" + "NIL = Datatype.In0 (Datatype.Numb 0)" + "CONS M N = Datatype.In1 (Datatype.Scons M N)" lemma CONS_not_NIL [iff]: "CONS M N \ NIL" and NIL_not_CONS [iff]: "NIL \ CONS M N" @@ -28,7 +28,7 @@ by (simp add: CONS_def In1_UN1 Scons_UN1_y) definition - "List_case c h = Datatype_Universe.Case (\_. c) (Datatype_Universe.Split h)" + "List_case c h = Datatype.Case (\_. c) (Datatype.Split h)" lemma List_case_NIL [simp]: "List_case c h NIL = c" and List_case_CONS [simp]: "List_case c h (CONS M N) = h M N" @@ -38,7 +38,7 @@ subsection {* Corecursive lists *} consts - LList :: "'a Datatype_Universe.item set \ 'a Datatype_Universe.item set" + LList :: "'a Datatype.item set \ 'a Datatype.item set" coinductive "LList A" intros @@ -50,8 +50,8 @@ unfolding LList.defs by (blast intro!: gfp_mono) consts - LList_corec_aux :: "nat \ ('a \ ('b Datatype_Universe.item \ 'a) option) \ - 'a \ 'b Datatype_Universe.item" + LList_corec_aux :: "nat \ ('a \ ('b Datatype.item \ 'a) option) \ + 'a \ 'b Datatype.item" primrec "LList_corec_aux 0 f x = {}" "LList_corec_aux (Suc k) f x = @@ -117,7 +117,7 @@ subsection {* Abstract type definition *} typedef 'a llist = - "LList (range Datatype_Universe.Leaf) :: 'a Datatype_Universe.item set" + "LList (range Datatype.Leaf) :: 'a Datatype.item set" proof show "NIL \ ?llist" .. qed @@ -125,20 +125,20 @@ lemma NIL_type: "NIL \ llist" unfolding llist_def by (rule LList.NIL) -lemma CONS_type: "a \ range Datatype_Universe.Leaf \ +lemma CONS_type: "a \ range Datatype.Leaf \ M \ llist \ CONS a M \ llist" unfolding llist_def by (rule LList.CONS) -lemma llistI: "x \ LList (range Datatype_Universe.Leaf) \ x \ llist" +lemma llistI: "x \ LList (range Datatype.Leaf) \ x \ llist" by (simp add: llist_def) -lemma llistD: "x \ llist \ x \ LList (range Datatype_Universe.Leaf)" +lemma llistD: "x \ llist \ x \ LList (range Datatype.Leaf)" by (simp add: llist_def) lemma Rep_llist_UNIV: "Rep_llist x \ LList UNIV" proof - have "Rep_llist x \ llist" by (rule Rep_llist) - then have "Rep_llist x \ LList (range Datatype_Universe.Leaf)" + then have "Rep_llist x \ LList (range Datatype.Leaf)" by (simp add: llist_def) also have "\ \ LList UNIV" by (rule LList_mono) simp finally show ?thesis . @@ -146,7 +146,7 @@ definition "LNil = Abs_llist NIL" - "LCons x xs = Abs_llist (CONS (Datatype_Universe.Leaf x) (Rep_llist xs))" + "LCons x xs = Abs_llist (CONS (Datatype.Leaf x) (Rep_llist xs))" lemma LCons_not_LNil [iff]: "LCons x xs \ LNil" apply (simp add: LNil_def LCons_def) @@ -167,7 +167,7 @@ by (simp add: LNil_def add: Abs_llist_inverse NIL_type) lemma Rep_llist_LCons: "Rep_llist (LCons x l) = - CONS (Datatype_Universe.Leaf x) (Rep_llist l)" + CONS (Datatype.Leaf x) (Rep_llist l)" by (simp add: LCons_def Abs_llist_inverse CONS_type Rep_llist) lemma llist_cases [cases type: llist]: @@ -176,7 +176,7 @@ | (LCons) x l' where "l = LCons x l'" proof (cases l) case (Abs_llist L) - from `L \ llist` have "L \ LList (range Datatype_Universe.Leaf)" by (rule llistD) + from `L \ llist` have "L \ LList (range Datatype.Leaf)" by (rule llistD) then show ?thesis proof cases case NIL @@ -195,7 +195,7 @@ definition "llist_case c d l = - List_case c (\x y. d (inv Datatype_Universe.Leaf x) (Abs_llist y)) (Rep_llist l)" + List_case c (\x y. d (inv Datatype.Leaf x) (Abs_llist y)) (Rep_llist l)" syntax (* FIXME? *) LNil :: logic @@ -217,17 +217,17 @@ Abs_llist (LList_corec a (\z. case f z of None \ None - | Some (v, w) \ Some (Datatype_Universe.Leaf v, w)))" + | Some (v, w) \ Some (Datatype.Leaf v, w)))" lemma LList_corec_type2: "LList_corec a (\z. case f z of None \ None - | Some (v, w) \ Some (Datatype_Universe.Leaf v, w)) \ llist" + | Some (v, w) \ Some (Datatype.Leaf v, w)) \ llist" (is "?corec a \ _") proof (unfold llist_def) let "LList_corec a ?g" = "?corec a" have "?corec a \ {?corec x | x. True}" by blast - then show "?corec a \ LList (range Datatype_Universe.Leaf)" + then show "?corec a \ LList (range Datatype.Leaf)" proof coinduct case (LList L) then obtain x where L: "L = ?corec x" by blast @@ -241,7 +241,7 @@ next case (Some p) then have "?corec x = - CONS (Datatype_Universe.Leaf (fst p)) (?corec (snd p))" + CONS (Datatype.Leaf (fst p)) (?corec (snd p))" by (simp add: split_def LList_corec) with L have ?CONS by auto then show ?thesis .. @@ -263,12 +263,12 @@ let "?rep_corec a" = "LList_corec a (\z. case f z of None \ None - | Some (v, w) \ Some (Datatype_Universe.Leaf v, w))" + | Some (v, w) \ Some (Datatype.Leaf v, w))" have "?corec a = Abs_llist (?rep_corec a)" by (simp only: llist_corec_def) also from Some have "?rep_corec a = - CONS (Datatype_Universe.Leaf (fst p)) (?rep_corec (snd p))" + CONS (Datatype.Leaf (fst p)) (?rep_corec (snd p))" by (simp add: split_def LList_corec) also have "?rep_corec (snd p) = Rep_llist (?corec (snd p))" by (simp only: llist_corec_def Abs_llist_inverse LList_corec_type2) @@ -281,8 +281,8 @@ subsection {* Equality as greatest fixed-point; the bisimulation principle. *} consts - EqLList :: "('a Datatype_Universe.item \ 'a Datatype_Universe.item) set \ - ('a Datatype_Universe.item \ 'a Datatype_Universe.item) set" + EqLList :: "('a Datatype.item \ 'a Datatype.item) set \ + ('a Datatype.item \ 'a Datatype.item) set" coinductive "EqLList r" intros @@ -291,7 +291,7 @@ (CONS a M, CONS b N) \ EqLList r" lemma EqLList_unfold: - "EqLList r = dsum (diag {Datatype_Universe.Numb 0}) (dprod r (EqLList r))" + "EqLList r = dsum (diag {Datatype.Numb 0}) (dprod r (EqLList r))" by (fast intro!: EqLList.intros [unfolded NIL_def CONS_def] elim: EqLList.cases [unfolded NIL_def CONS_def]) @@ -612,7 +612,7 @@ have "(?lhs M, ?rhs M) \ {(?lhs N, ?rhs N) | N. N \ LList A}" using M by blast then show ?thesis - proof (coinduct taking: "range (\N :: 'a Datatype_Universe.item. N)" + proof (coinduct taking: "range (\N :: 'a Datatype.item. N)" rule: LList_equalityI) case (EqLList q) then obtain N where q: "q = (?lhs N, ?rhs N)" and N: "N \ LList A" by blast @@ -635,7 +635,7 @@ proof - have "(?lmap M, M) \ {(?lmap N, N) | N. N \ LList A}" using M by blast then show ?thesis - proof (coinduct taking: "range (\N :: 'a Datatype_Universe.item. N)" + proof (coinduct taking: "range (\N :: 'a Datatype.item. N)" rule: LList_equalityI) case (EqLList q) then obtain N where q: "q = (?lmap N, N)" and N: "N \ LList A" by blast diff -r cb6ae81dd0be -r 58693343905f src/HOL/Tools/datatype_package.ML --- a/src/HOL/Tools/datatype_package.ML Sun Oct 01 22:19:21 2006 +0200 +++ b/src/HOL/Tools/datatype_package.ML Sun Oct 01 22:19:23 2006 +0200 @@ -927,7 +927,7 @@ fun gen_add_datatype prep_typ err flat_names new_type_names dts thy = let - val _ = Theory.requires thy "Datatype_Universe" "datatype definitions"; + val _ = Theory.requires thy "Datatype" "datatype definitions"; (* this theory is used just for parsing *) diff -r cb6ae81dd0be -r 58693343905f src/HOL/Tools/datatype_rep_proofs.ML --- a/src/HOL/Tools/datatype_rep_proofs.ML Sun Oct 01 22:19:21 2006 +0200 +++ b/src/HOL/Tools/datatype_rep_proofs.ML Sun Oct 01 22:19:23 2006 +0200 @@ -43,13 +43,13 @@ new_type_names descr sorts types_syntax constr_syntax case_names_induct thy = let val Datatype_thy = ThyInfo.the_theory "Datatype" thy; - val node_name = "Datatype_Universe.node"; - val In0_name = "Datatype_Universe.In0"; - val In1_name = "Datatype_Universe.In1"; - val Scons_name = "Datatype_Universe.Scons"; - val Leaf_name = "Datatype_Universe.Leaf"; - val Numb_name = "Datatype_Universe.Numb"; - val Lim_name = "Datatype_Universe.Lim"; + val node_name = "Datatype.node"; + val In0_name = "Datatype.In0"; + val In1_name = "Datatype.In1"; + val Scons_name = "Datatype.Scons"; + val Leaf_name = "Datatype.Leaf"; + val Numb_name = "Datatype.Numb"; + val Lim_name = "Datatype.Lim"; val Suml_name = "Datatype.Suml"; val Sumr_name = "Datatype.Sumr";